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A payoff function for a player is a mapping from the cross-product of players' strategy spaces to that player's set of payoffs (normally the set of real numbers, where the number represents a cardinal or ordinal utility—often cardinal in the normal-form representation) of a player, i.e. the payoff function of a player takes as its input a ...
"A best response to a coplayer’s strategy is a strategy that yields the highest payoff against that particular strategy". [9] A matrix is used to present the payoff of both players in the game. For example, the best response of player one is the highest payoff for player one’s move, and vice versa.
Risk dominance and payoff dominance are two related refinements of the Nash equilibrium (NE) solution concept in game theory, defined by John Harsanyi and Reinhard Selten.A Nash equilibrium is considered payoff dominant if it is Pareto superior to all other Nash equilibria in the game. 1 When faced with a choice among equilibria, all players would agree on the payoff dominant equilibrium since ...
I think the colour-coded matrix would be useful pedagogically to illustrate which payoffs are whose when the matrix is being explained (i.e. in an article about payoff matrices), but in all other cases (when a payoff matrix is being used not for its own sake), I'd prefer to see the standard ordered pair.
The rule goes as follows: if the first payoff number, in the payoff pair of the cell, is the maximum of the column of the cell and if the second number is the maximum of the row of the cell - then the cell represents a Nash equilibrium.
The payoffs are provided in the interior. The first number is the payoff received by the row player (Player 1 in our example); the second is the payoff for the column player (Player 2 in our example). Suppose that Player 1 plays Up and that Player 2 plays Left. Then Player 1 gets a payoff of 4, and Player 2 gets 3.
The excess of for a coalition is the quantity (); that is, the gain that players in coalition can obtain if they withdraw from the grand coalition under payoff and instead take the payoff (). The nucleolus of v {\displaystyle v} is the imputation for which the vector of excesses of all coalitions (a vector in R 2 N {\displaystyle \mathbb {R ...
This is a documentation subpage for Template:Payoff matrix. It may contain usage information, categories and other content that is not part of the original template page. Usage